Based on the electromagnetic theory, an electromagnetic wave not only has the linear momentum along the beam propagation direction but also has the angular momentum which is perpendicular to the beam propagation direction [1]}. The OAM is one part of the angular momentum whose electromagnetic fields are characterized by a wavefront that is shaped as a helix, i.e., \(exp \left( { - il\phi } \right)\) , where \(\phi \)  is the transverse azimuthal angle and \(l\)  is the OAM state, i.e., an unbounded integer. The OAM state \(l\)  implies a \(2\pi l\)  phase delay over one revolution of a beam in millimeter wave communications. Moreover, beams with different OAM states are mutually orthogonal and thus can be multiplexed together along the same beam axis for propagation. Thereby, the capacity of wireless communication systems could be obviously improved by the OAM technology [1]}, [3]}. Although the OAM feature of electromagnetic wave has been indicated in early years of 20th century [4]}, until recent years the OAM technology has been used for optical communications [3]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. Laser light with Laguerre-Gaussian amplitude distribution was first found to have an OAM and the Laguerre-Gaussian mode can be transformed from the Hermite-Gaussian mode in astigmatic optical systems [6]}. Utilizing the OAM technology, information was encoded into a light beam and was transmitted by free space communication experiments [3]}. Using Laguerre-Gaussian mode beam, the spatial mode division multiplexing with two OAM states was first demonstrated to achieve 10 Gbps transmission rate in optical communications [7]}. By Combining with low-density parity-check (LDPC) codes, OAM-based modulation schemes were proposed to realize high speed transmissions over strong atmospheric turbulence channels in deep-space and near-earth optical communications [8]}. Modulating 16-quadrature-amplitude-modulation signals over four OAM states, a spectral efficiency of 25.6 bit/s/Hz was implemented by polarization-multiplexed multiple OAM optical communication systems [9]}. A 2-Tbit/s data link was presented in free space optical communication systems using two orthogonal OAM states with 25 wavelength division multiplexed channels on each state [10]}. In a 1.1 kilometer transmission scenario over an optical fiber, 1.6 Tbit/s data transmission rate was demonstrated for optical communications with two OAM states over 10 wavelengths [11]}.
